Unequal Error Protection Codes for Wavelet Image Transmission over W-CDMA, AWGN and Rayleigh Fading Channels MINH H. LE and RANJITH LIYANA-PATHIRANA School of Engineering and Industrial Design College of Science, Technology and Environment University of Western Sydney Second Avenue, Kingswood, 2747, N.S.W. AUSTRALIA. http://www.geocities.com/minhle_uws http://www.uws.edu.au/schools/seid/programs/engineering/mce/drr.htm Abstract: - Wavelets are being utilized in various communications applications either as an alternative to short time Fourier transform for spectral analysis of non-stationary data or as a new tool to bridge between time domain and frequency domain analysis. A wavelet-based algorithm for image compression with four levels of unequal error protection (UEP) codes over wide-band code division multiple access (W-CDMA), additive white Gaussian noise (AWGN) and Rayleigh fading channels are analysed. The utilization of Wavelets has come out to be a powerful method for compress images. The wavelet transform compression technique has shown to be more appropriate to low bit rate applications, producing better quality output for the compressed frame of video. The proposed algorithms of the 2-D wavelet packet transform (2-D WPT) and the embedded zero-tree wavelet (EZW) coder are investigated. Key-Words: - Unequal Error Protection Codes, Embedded Zero-Tree Wavelet, Two Dimensional Wavelet Packet, Wide-Band Code Division Multiple Access, Additive White Gaussian Noise, Rayleigh Fading Channel. 1. Introduction The wavelet functions are being utilized for harmonic analysis, signal representation, speech and video bandwidth compression, multiresolution signal processing, and signal design in various coding and communication applications. The early success of wavelets in commercial applications was mainly with efficient compression techniques on signals such as voice and video. This was due to the logarithmicscale decomposition in frequency, which fits naturally in many of the sound and image reconstruction studies. Wavelet theory covers quite a large area. It treats both the continuous and discrete time cases [1]. The introduction of the embedded zero-tree concept for wavelet-based image compression has generated a significant improvement in performance compared to previous image coding methods. A refinement of the EZW approach, called set partitioning into hierarchical trees (SPIHT) by Said and Pearlman, is the most well known EZW derivative. While SPIHT enjoys a good ratedistortion performance for still images with comparatively low complexity, it is quite fragile against bit errors in noisy communication channels. Direct sequence signal acquisition in W-CDMA environment is estimated. A digital matched filter is presented and investigated for direct sequence spread-spectrum systems [2]. The proposed scheme accomplishes unequal error protection by encoding the data according to the significance of the information and switching between four codes. The coding scheme presents four levels of error protection for different sets of bits in a transmitted symbol using W-CDMA, AWGN and Rayleigh fading channels. The scheme uses the different pseudo-noise codes of digital matched filter synchronizer to make up four levels of unequal error protection codes. The scheme also shows design flexibility so that it is easily modified to accommodate different needs for error protection in various data transmission systems. The detailed design procedure and the performance of four unequal error protection codes are presented. The unequal error protection with bits of different significance for data transmission is achieved in this scheme. It was shown that four levels of different error protections were easily accomplished with the digital matched filter pseudo-noise code synchronizer systems over AWGN and Rayleigh fading channels by providing the coded detection at the receiver. The scheme provides the capability of multi-level error protection without complexity as compared to regular digital matched filter pseudo-noise code schemes.
2. Unequal Error Protection Codes with Wavelet Image Transmission over W-CDMA, AWGN and Rayleigh Fading Channels The unequal error protection with bits of different significance for data transmission is achieved in these schemes. It was shown that four levels of different error protections were easily accomplished with the digital matched filter pseudo-noise code synchronizer systems by providing the coded detection at the receiver. The scheme provides the capability of multi-level error protection without complexity as compared to regular digital matched filter pseudonoise code schemes. Figure 1 illustrates the block diagram of UEP codes with wavelet image compression over W-CDMA, AWGN and Rayleigh fading channels Encoder. Figure 2 shows the block diagram of UEP codes with wavelet image compression over W-CDMA, AWGN and Rayleigh fading channels Decoder. 2.1. The Embedded Zero-Tree Wavelet Coding Discrete wavelet transform is becoming popular in many image/video applications due to the unique feature of multi-resolution representation. After the wavelet transform of an image, the important data is concentrated in the upper left corner that corresponds to the low frequency range of the wavelet coefficients. The remaining data in the high frequency domain is not as significant. The embedded zero-tree wavelet (EZW) algorithm exploits the important hypothesis that if a wavelet coefficient at a coarse scale is insignificant with respect to a threshold, then all the wavelet coefficients of the same orientation in the spatial location at finer scales are likely to be insignificant with respect to the same threshold. Because wavelet decompositions offer space frequency representations of images, i.e., low frequency coefficients have large spatial support, (good for representing large image background regions), whereas high frequency coefficients have small spatial support (good for representing spatially local phenomena such as edges), the wavelet representation calls for new quantization strategies that go beyond traditional subband coding techniques to exploit this underlying space frequency image characterization. Fig. 1 Block Diagram of UEP Codes for Wavelet Image Transmission over W-CDMA, AWGN and Rayleigh fading channels Encoder Shapiro made a breakthrough in 1993 with his embedded zero tree wavelet-coding algorithm [3]. Since then a new class of algorithms has been developed that achieve significantly improved performance over the EZW coder. In particular, Said and Pearlman s work on set partitioning in hierarchical trees (SPIHT) [4], which improves the EZW coder, has established zero tree techniques as the current state of the art of wavelet image coding since the SPIHT algorithm proves to be very successful for both lossy and lossless compression. A wavelet coefficient tree is defined as the set of coefficients from different bands that represent the same spatial region in the image. A wavelet image representation can be thought of as a tree structured spatial set of coefficients. Figure 3 illustrates three levels wavelet decomposition. The lowest frequency band of the decomposition is represented by the root nodes (top left) of the tree (LL 3 ), the highest frequency bands by the leaf nodes (bottom right) of the tree, and each parent node represents a lower frequency component than its children. Except for a root node, which has only three children nodes, each parent node has four children nodes, the 2x2 region of the same spatial location in the immediately higher frequency band.
and one high frequency signal, we would still be able to understand the words only using the low frequency signal. However, if we listened to high frequency signal, we would only hear noise and hisses, particularly in the pronunciation of the c,h,s,t letters. Figure 4 illustrates the block diagram of twodimensional wavelet packet transform. Fig. 2 Block Diagram of UEP Codes for Wavelet Image Transmission over W-CDMA, AWGN and Rayleigh fading channels Decoder Fig. 3 Three Level Wavelet Decomposition of The Image 2.2. The 2-Dimensional Wavelet Packet Discrete wavelet transform (DWT) is applied to images; it is advantage of the fact that images are composed of low frequency components and high frequency components. Low frequency components give an image its foundation, or character, while high frequency components give an image it is fine details or nuances. If we thought of this in terms of sound, say that for example we were sampling a human voice for transform over some digital means. When this signal is spit into two: one low frequency signal Fig. 4 Block Diagram of The 2-D Wavelet Packet The output from the low pass filter produces and approximation of the signal based on the low frequency detail coefficients. The output from the high pass filter produces the fine details of the image, that when put together will form the original image. However, these values are down-sampled. This means that the output of either filter has every second coefficient dropped. This effectively halves the number of coefficients from each filter. Nevertheless, at the reconstruction side, this can produce some distortion, but if the filters are chosen carefully then perfect reconstruction can occur. One of the aspects that makes wavelets so suited to image coding is that the filtering process can be iterated repeatedly, allowing us to break up an image into various lower resolution versions or multilevel decomposition. This is especially useful when image compression is being considered, because we can make trade-off between useful image information and plain noise. Typically, the way in which this is conducted is by filtering the output of the Low Frequency Decomposing Filter with the same wavelet function. The low frequency coefficients of this output may again be filtered, extracting more information and so on. Now, because there is a down sampling routine done after each filtering process, the theoretical limit that stops us from iterating is until we reach one DWT coefficient. In general, the more levels of decomposition we have, the better the compression, although loss of quality too. However, this will depend on the particular image size. Obviously, an image of 128 by 128 pixels will not be able to be decomposed as much levels as an image of size 512 by 512 pixels [5].
2.3. Unequal Error Protection Codes With Four Levels Masnick and Wolf [6] first introduced the concept of unequal error protection codes in 1969. Their approach influenced different techniques of protection of codeword symbols, restricting the known facts to systematic codes. Dunning and Robbins [7] presented a more general approach in 1978. Their accomplishment pointed out that encoding is crucial for the unequal error protection properties of a code. Consequently, the two different encodings of the same code are not similar regarding their unequal error protection properties. The structure of codes with unequal error protection differs fairly from the ordinary code. The ordinary codes are designed to obtain uniform distance distribution to provide a large minimum distance. The unequal error protection codes have the codewords joined in clusters. Unequal error protection codes are used in many speech and image coding schemes; some of the message positions are largely sensitive to channel errors while some others exhibit a very small amount of sensitivity. In view of making the best use of channel redundancy, unequal error protection codes are applied. In a frequency band limited situation, such coding and the modulation should be integrated. The necessity for unequal error protection arises in applications where the transmitted data is a coded signal such as speech, audio, image or video [6]. The unequal error protection with bits of different significance for data transmission is achieved in this scheme. It was shown that four levels of different error protections were easily accomplished with the digital matched filter pseudo-noise code synchronizer systems by providing the coded detection at the receiver. The scheme provides the capability of multi-level error protection without complexity as compared to regular digital matched filter pseudonoise code schemes. 2.4. Wide-Band Code Division Multiple Access Channels The W-CDMA is technique in which users share the channel by employing different spreading codes. In W-CDMA systems, all the users occupy the same frequency band at the same time. This is in contrast to frequency division multiple access (FDMA) and time division multiple access (TDMA) schemes in which the signals occupy the channel at disjoint frequencies or times, respectively. In W-CDMA systems, each transmitter has a different spreading code that is known by the intended receiver. For effective operation, the cross correlation between code used by different users should be minimized so that the despreading process will reject most of the multi-user interference. W-CDMA systems can be implemented using either frequency hopping (FH) or direct sequence (DS) spread spectrum techniques, although DS is by far the most popular choice. One reason for this is that when multiple approaches is generally more computationally intensive than the synchronous approach. The basis function to be used as the spreading waveform is determined by a pseudo-noise (PN) sequence and is allowed to change with each incoming data bit. Since both the transmitter and receiver are assumed to know which spreading function is used, and, since these codes are known to be orthogonal. Each user is assigned a different spreading code, i.e., transform basis function, and allowed to transmit over the same channel. If all users transmit synchronously, the orthogonality of the spreading waveforms ensures that there is no interference between users [8]. The use of direct sequence spread spectrum (DS- SS) in mobile communications has been growing considerably over the past few years. DS-SS is especially attractive in this situation due to its inherent antimultipath capabilities. Pseudo-noise (PN) code acquisition is essential in any DS-SS system, where a synchronized replica of the transmitted PN code is required in the receiver to despread the received signal and allow the recovery of data sequence. The proposed digital matched filter (DMF) achieves a mean time to acquisition comparable to that obtained by the conventional MF allows an unlimited period of integration without complexity increase and some advantages in terms of probabilities of correct acquisition and false alarm. Since the nature of direct sequence spread spectrum signals is digital, digital matched filters provide a straightforward way of implementing correlation in noncoherent receivers for signals of that kind. Digital concepts provide most flexibility, which is required for easy adaptability to changing waveforms. This can be of paramount importance for the exploitation of the anti-interference and anti-eavesdropping capabilities of such systems. Digital matched filter is one of the most critical components incorporated in the VLSI transceiver in terms of power dissipation. 2.5. Unequal Error Protection Codes with Wavelet Image Transmission over W-CDMA, AWGN and Rayleigh Fading Channels The W-CDMA, AWGN and Rayleigh fading channels with unequal error protection are investigated with four levels of significance for use with data stream of information. The proposed scheme accomplishes unequal error protection by encoding the data according to the significance of the information and switching between four codes. The coding scheme presents four levels of error protection for different sets of bits in a transmitted symbol using W-CDMA, AWGN and Rayleigh fading channels.
The scheme uses the different pseudo-noise codes of digital matched filter synchronizer to make up four levels of unequal error protection codes. The scheme also shows design flexibility so that it is easily modified to accommodate different needs for error protection in various data transmission systems. The detailed design procedure and the performance of four unequal error protection codes are presented. The four levels of unequal error protection codes with four different levels of unequal error protection codes are designed for this digital matched filter pseudo-noise code synchronizer scheme. The first level is the lowest error protection level with easiest level of digital matched filter pseudo-noise code synchronizer. The second level is the lower level with easier level of digital matched filter pseudo-noise code synchronizer. The third level is the higher level with harder level of digital matched filter pseudonoise code synchronizer. The fourth level is the highest level with hardest level of digital matched filter pseudo-noise code synchronizer. For the Embedded Zero-Tree Wavelet Coding, the four levels of unequal error protection codes with four significant levels of unequal error protection codes are proposed for this digital matched filter pseudo-noise code synchronizer scheme. From figure 3, the first level or the LL 3 is the lowest error protection level with no encoding. The second level or the HL 3, LH 3, HH 3 is the lower error protection level with easiest level of digital matched filter pseudo-noise code synchronizer. The third level or the HL 2, LH 2, HH 2 is the higher error protection level with easier level of digital matched filter pseudonoise code synchronizer. The fourth level or the HL 1, LH 1, HH 1 is the highest error protection level with harder level of digital matched filter pseudo-noise code synchronizer [3]. For the 2-D Wavelet Packet, the four levels of unequal error protection codes with four different levels of unequal error protection codes are designed for this digital matched filter pseudo-noise code synchronizer scheme. Figure 4 illustrates the block diagram of two-dimensional wavelet packet transform. The first level or the average signal is the lowest error protection level with easiest level of digital matched filter pseudo-noise code synchronizer. The second level or the horizontal image features is the lower error protection level with easier level of digital matched filter pseudo-noise code synchronizer. The third level or the vertical image features is the higher error protection level with harder level of digital matched filter pseudonoise code synchronizer. The fourth level or the diagonal image features is the highest error protection level with hardest level of digital matched filter pseudo-noise code synchronizer. 3. Experimental Results The QCIF images with compression rate of 0.312 bits/pixel are examined. The W-CDMA system obtains a bandwidth of 5MHz and will also be in many indoor achievements. The various sections of a compressed image obtain different importance and error sensitivity. The W-CDMA, AWGN, and Rayleigh fading channels with unequal error protection codes are considered with four levels of significance for operating with data stream of information. The proposed scheme achieves unequal error protection by encoding the data according to the significance of the information and switching between four codes. The coding scheme introduces four levels of error protection for different sets of bits in a transmitted symbol functioning W-CDMA, AWGN, and Rayleigh fading channels. The proposed scheme applies the different pseudo-noise codes of digital matched filter synchronizer to construct four levels of unequal error protection codes. The proposed scheme illustrates the design flexibility so that it is easily modified to accommodate different needs for error protection in various data transmission systems. The functioning estimation of four unequal error protection codes with W-CDMA, AWGN, and Rayleigh fading channels are evaluated. In the Embedded Zero-Tree Wavelet Coding, the four levels of unequal error protection codes with four important levels of unequal error protection codes are proposed for this digital matched filter pseudo-noise code synchronizer scheme. As figure 3, the first level or the LL 3 is the lowest error protection level with no encoding. The second level or the HL 3, LH 3, HH 3 is the lower error protection level with easiest level of digital matched filter pseudo-noise code synchronizer. The third level or the HL 2, LH 2, HH 2 is the higher error protection level with easier level of digital matched filter pseudo-noise code synchronizer. The fourth level or the HL 1, LH 1, HH 1 is the highest error protection level with harder level of digital matched filter pseudo-noise code synchronizer. In the 2-D Wavelet Packet, the four levels of unequal error protection codes with four significant levels of unequal error protection codes are designed for this digital matched filter pseudonoise code synchronizer scheme. From the figure 4, the first level or the average signal is the lowest error protection level with easiest level of digital matched filter pseudo-noise code synchronizer. The second level or the horizontal image features is the lower error protection level with easier level of digital matched filter pseudo-noise code synchronizer. The third level or the vertical image features is the higher error protection level with harder level of digital matched filter pseudo-noise code synchronizer. The fourth level or the diagonal image features is the highest error protection level with hardest level of
digital matched filter pseudo-noise code synchronizer. Matlab programs are written to simulate the outcomes of the four levels of UEP codes with wavelet image compression over W-CDMA, AWGN and Rayleigh fading channels. The peak signal to noise ratio is calculated. The objective image quality has been evaluated using peak signal to noise ratio, which is defined as follows: PSNR=10*log 10 ((Peak Signal Value) 2 /Mean Square Error) where, Peak Signal Value=255 for an 8 bits/pixel image. Mean Square Error=(1/(NxN)) (x ij -y ij ) 2 ij x ij -y ij =value of pixel (i,j) in the original and reconstructed images respectively. NxN=number of pixels in the image. Fig. 5 (a) Fig. 5 (b) Fig. 5 (a) The original Lena image in QCIF (b) The original Barbara image in QCIF The results of Lena images in QCIF (176x144) are illustrated in figure 6 and figure 7. The results of Barbara images in QCIF (176x144) are illustrated in figure 8 and figure 9. The table of outcomes of tested Lena images is tabulated in the table 1. Lena images in QCIF with compression rate of 0.312 (bits/pixel) of Four levels UEP for EZW of Four levels UEP for 2-D Wavelet Packet AWGN channels 10.17 10.06 Rayleigh fading channels 30.12 30.04 Fig. 6 (a) Fig. 6 (b) Fig. 6 The reconstructed Lena images with four levels of Embedded Zerotree Wavelet transform over (a) W- CDMA and AWGN channels; PSNR=10.17 db (b) Rayleigh fading channels; PSNR=30.12 db Table 1: The outcomes of tested Lena images The table of outcomes of tested Barbara images is tabularized in the table 2. Barbara images in QCIF with compression rate of 0.312 (bits/pixel) of Four levels UEP for EZW of Four levels UEP for 2-D Wavelet Packet AWGN channels 10.16 10.05 Rayleigh fading channels 30.12 29.99 Fig. 7 (a) Fig. 7 (b) Fig. 7 The reconstructed Lena images with four levels of 2-D Wavelet Packet over (a) W-CDMA and AWGN channels; PSNR=10.06 db (b) W- CDMA and Rayleigh fading channels; PSNR=30.04 db Table 2: The outcomes of tested Barbara images The original tested images of Lena and Barbara in QCIF (176x144) are illustrated in figure 5. Fig. 8 (a) Fig. 8 (b)
Fig. 8 The reconstructed Barbara images with four levels of Embedded Zerotree Wavelet transform over (a) AWGN channels; PSNR=10.16 db (b) Rayleigh fading channels; PSNR=30.12 db unequal error protection codes. The scheme also shows design flexibility so that it is easily modified to accommodate different needs for error protection in various data transmission systems. The detailed design procedure and the performance of four unequal error protection codes are presented. References: [1] I. Daubechies, The Wavelet, Time Frequency Localization and Signal Analysis, IEEE Trans. On Info. Theory, Vol. 36, pp. 961-1005. [2] Martin Vetterli, Jelena Kavacevic, Wavelets and Subband Coding, Prentice Hall, Signal Processing Series, 1995. Fig. 9 (a) Fig. 9 (b) Fig. 9 The reconstructed Barbara images with four levels of 2-D Wavelet Packet over (a) W- CDMA and AWGN channels; PSNR=10.05 db (b) Rayleigh fading channels; PSNR=29.99 db 4. Conclusions The embedded zero tree wavelet coding structure embodied in the celebrated SPIHT algorithm as a representative of this latter class, we have detailed its operation by using a simple illustrative example. We have also described the role of wavelet packets as a simple but powerful generalization of the wavelet decomposition, in order to offer a more robust and adaptive transform image-coding framework. The wavelet image compression with UEP codes over W- CDMA, AWGN and Rayleigh fading channels are investigated. DWT computation is studied with Daubechies filters set, Daubechies derivation, orthogonal filter coefficient extraction and apply the DWT to images. Specifically, the EZW algorithm, the 2-D wavelet packet transform, and the entropy coding are analyzed with UEP codes over W-CDMA, AWGN and Rayleigh fading channels. The direct sequence signal acquisition in W-CDMA environment with the proposed digital matched filter synchronizer for fast code acquisition have been presented and analysed. Performance evaluation of wavelet image compression with four levels of UEP codes over W- CDMA, AWGN and Rayleigh fading channels are presented. The proposed scheme accomplishes unequal error protection by encoding the data according to the significance of the information and switching between four codes. The coding scheme presents four levels of error protection for different sets of bits in a transmitted symbol using W-CDMA, AWGN and Rayleigh fading channels. The scheme uses the different pseudo-noise codes of digital matched filter synchronizer to make up four levels of [3] J. Shapiro, Embedded Image Coding Using Zero Trees of Wavelet Coefficients, IEEE Trans. Signal Process. 41, 3445-3462, 1993. [4] A. Said and W. A. Pearlman, A New, Fast, and Efficient Image Codec Based On Set Partitioning In Hierarchical Trees, IEEE Trans. Circuits Syst. Video Technol. 6, 243-250, 1996. [5] J. Villasenor, B. Belzer and J. Liao, Wavelet Filter Evaluation for Image Compression, IEEE Transactions, August 1995. [6] B. Masnick and J. Wolf, On Linear Unequal Error Protection Codes, IEEE Trans, Inform, Theory, Vol. IT-13, pp. 600-607, July 1967. [7] L. A. Dunning; W. E. Robbins, Optimal Encodings of Linear Block Codes for Unequal Error Protection, Information and Control 37, pp. 150 177, 1978. [8] Iinatti J. and Leppanen P., Matched Filter Synchronization of DS Receiver in Continuous Tone Jamming, ISSSTA90, pp. 30-35, 1990. Minh H. Le received the M.E.(Honor) degree, transferred to Ph.D. degree, he is currently a Ph.D. student in Electrical Engineering, School of Engineering and Industrial Design, College of Science, Technology and Environment, University of Western Sydney, Nepean, Kingswood, NSW, Australia. He is a member of the IEEE. His research interests include error control coding, channel coding and trellis coded modulation, image/video processing, wavelet image compression, W-CDMA, communication systems, digital mobile communications, communication fading channel modeling. Dr. Ranjith Liyanapathirana received the B.Sc.Eng.(Hons) degree in Electronic and Telecommunication Engineering from University of Moratuwa, Sri Lanka, in 1981, M.Eng. and Ph.D. degrees in Electrical Engineering (Communications and Signal Processing), from Memorial University of Newfoundland, Canada, in 1987, and 1995. He is currently a senior lecturer in Electrical Engineering, School of Engineering and Industrial Design, College of Science, Technology and Environment, University of Western Sydney, Nepean, Kingswood, NSW, Australia. He is a member of the IEEE. His research interests include digital mobile communications, information theory and coding, error control coding, channel coding and trellis coded modulation, image/video processing, wavelet video, CDMA, communication systems, communication fading channel modeling, amateur radio (VK6BHV).